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Chapter 11: Problem 109

Thyroxine, an important hormone that controls the rate of metabolism in the body, can be isolated from the thyroid gland. When 0.455 g thyroxine is dissolved in 10.0 g benzene, the freezing point of the solution is depressed by \(0.300^{\circ} \mathrm{C}\) . What is the molar mass of thyroxine? See Table \(11.5 .\)

Short Answer

Expert verified
The molar mass of thyroxine is approximately \(776 \: \text{g/mol}\).

Step by step solution

01

Calculate the molality (m) of the solution

To calculate the molality of the solution, we will use the formula ΔT = K_f * m, where ΔT is the freezing point depression, K_f is the freezing point depression constant (in °C/molal) for the solvent, and m is the molality of the solution. Given, ΔT = 0.300°C and for benzene, K_f = 5.12°C/molal (from Table 11.5). Rearrange the formula to solve for m: m = ΔT / K_f m = 0.300°C / 5.12°C/molal m = 0.0586 molal
02

Calculate the moles of thyroxine in the solution

Now we can calculate the moles of thyroxine in the solution using the formula molality = moles solute / mass of solvent in kg. Given, weight of thyroxine = 0.455 g and weight of benzene = 10.0 g. First, convert the mass of benzene to kg: 10.0 g = 0.010 kg Rearrange the formula to solve for moles of solute: moles solute = molality * mass of solvent in kg moles solute = 0.0586 molal * 0.010 kg moles solute = 0.000586 mol
03

Find the molar mass of thyroxine

Now that we have the moles of thyroxine, we can find its molar mass by using the formula molar mass = mass / moles. Molar mass of thyroxine = 0.455 g / 0.000586 mol Molar mass of thyroxine ≈ 776 g/mol Thus, the molar mass of thyroxine is approximately 776 g/mol.

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Most popular questions from this chapter

a. Calculate the freezing-point depression and osmotic pressure at $25^{\circ} \mathrm{C}\( of an aqueous solution containing 1.0 \)\mathrm{g} / \mathrm{L}$ of a protein (molar mass \(=9.0 \times 10^{4} \mathrm{g} / \mathrm{mol} )\) if the density of the solution is 1.0 \(\mathrm{g} / \mathrm{cm}^{3}\) b. Considering your answer to part a, which colligative property, freezing- point depression or osmotic pressure, would be better used to determine the molar masses of large molecules? Explain.

When pure methanol is mixed with water, the resulting solution feels warm. Would you expect this solution to be ideal? Explain.

Consider an aqueous solution containing sodium chloride that has a density of 1.01 \(\mathrm{g} / \mathrm{mL}\) . Assume the solution behaves ideally. The freezing point of this solution at 1.0 \(\mathrm{atm}\) is $-1.28^{\circ} \mathrm{C}$ . Calculate the percent composition of this solution (by mass).

The normal boiling point of diethyl ether is \(34.5^{\circ} \mathrm{C}\) . A solution containing a nonvolatile solute dissolved in diethyl ether has a vapor pressure of 698 torr at \(34.5^{\circ} \mathrm{C} .\) What is the mole fraction of diethyl ether in this solution?

The normal boiling point of methanol is \(64.7^{\circ} \mathrm{C} .\) A solution containing a nonvolatile solute dissolved in methanol has a vapor pressure of 556 torr at \(64.7^{\circ} \mathrm{C} .\) What is the mole fraction of methanol in this solution?
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